For testing android traffic encryption I have configured a VPN client in my phone. What simple test I can perform in my home wifi network to verify that the traffic is really encrypted and secure?
If the server is located somewhere else, you can check if the traffic is being tunneled through the VPN server by checking what IP address you are coming from. Visit a site like http://www.whatismyip.com/ with and without your VPN software enabled on your phone and see if it is a different IP address displayed.
Capturing the traffic from the air is a little bit tricky involving some steps like having a wireless card that supports monitor mode and software that makes use of the monitor mode.
A simple way of inspecting all the traffic to and from your phone is to pass it through a device where you can run a pocket inspection tool. Here is a tutorial about using Internet Connection Sharing in Windows to set up a hotspot on your PC: http://lifehacker.com/5369381/turn-your-windows-7-pc-into-a-wireless-hotspot. Connectify Hotspot is also a simple software to use: http://www.connectify.me/hotspot/.
Once the traffic from your phone passes through your PC, you can use Wireshark on your PC to inspect the traffic for unencrypted text.